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Re: factorial of (1/2)
Damn. This is how it goes. Just calculate
Gamma(3/2)
by integrating and then just use the general definition
x! = Gamma(x+1)
for all real x.
Added after 8 minutes:
I see. hmm.
Added after 25 minutes:
Can't say that I see how to do the integral by just...
Re: factorial of (1/2)
Yes the value comes from the gamma function.
The factorial n! coincides with the gamma function at positive integer values. So if one equates the factorial function on all positive reals with the gamma function, then one can say that
(1/2)! = sqrt(pi)/2
even though...
Re: INFINITY
countable infinity means "can be put into a one to one corespondens with the natural numbers" and uncountable means that this impossible. So the integers {..,-3,-2,-1,0,1,2,3,...} are e.g. countable because we can make the mapping
0 -> 0
1 -> 1
2 -> -1
3 -> 2
4 -> -2
...
The...
The answers above seem to answer the question: when is a function integrable?
One answer is e.g. that all continuos functions are Riemann integrable on a closed interval. If we use another definition of integral e.g. Lebesgue integral then we will get a another set of integrable functions.
I...
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